COMPLETE SECONDARY ALGEBRA BY GEORGE EGBERT FISHER, M.A., PH.D. AND ISAAC J. SCHWATT, Pí.D. ASSISTANT PROFESSORS OF MATHEMATICS IN THE QUADRATICS AND BEYOND New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. 1916 All rights reserved HARVARD COPYRIGHT, 1901, BY FISHER AND SCHWATT. First printed elsewhere. Reprinted July, 1902; Frencik CHAPTER XVIII. QUADRATIC EQUATIONS. 1. A Quadratic Equation is an equation of the second degree in the unknown number or numbers. E.g., x2=25, x2-5x+6=0, x2 + 2xy = 7. A Complete Quadratic Equation, in one unknown number, is one which contains a term (or terms) in 22, a term (or terms) in x, and a term (or terms) free from x, as x2- 2 ax+b=cx−d. A Pure Quadratic Equation is an incomplete quadratic equation which has no term in x, as x2 — 9 = 0. Pure Quadratic Equations. 2. Ex. 1. Solve the equation 6 x2 - 7 = 3x2 + 5. Transferring 3x2 to the first member, and 7 to the second member, 6 x2-3x2=5+7, The value of x is a number whose square is 4. But Therefore 224, and (-2)2=4. x= ± 2. 3. This example illustrates the following principle of equiva lent equations: The positive square root of the first member of an equation may be equated in turn to the positive and to the negative square root of the second member. |